CN109088770A - A kind of Mechatronic Systems Internet modeling method based on self-adaptive symbol transfer entropy - Google Patents
A kind of Mechatronic Systems Internet modeling method based on self-adaptive symbol transfer entropy Download PDFInfo
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Abstract
The process industry complex electromechanical systems Internet modeling method based on self-adaptive symbol transfer entropy that the invention discloses a kind of, the common parameter of acquisition time sequence symbol on the basis of multivariate space reconstruct, the probability density of original time series and distribution are estimated using self-adaptive kernel density estimation method, and equiprobability division is carried out to sequence, by obtaining optimal symbol numbers and demarcation interval, realize the carry out coarse symbol expression of original series, to improve the accuracy that interactive information between variable is estimated, transfer entropy analysis is carried out to the symbol sebolic addressing of monitored parameters, and carry out the calculating of net amount of transmitted information, with basic parameter needed for obtaining system interaction network modelling, and establish the network model of reflection real system bottom interaction mechanism.The network model will be assessed for system mode, and fault propagation analyzes and diagnoses decision and provides foundation, so that it is horizontal to improve the science of process industry complex electromechanical systems safe and reliable operation and intelligent decision making under complex working condition.
Description
Technical field
The present invention relates to complex electromechanical systems military service security state evaluation fields, and in particular to one kind is based on self-adaptive symbol
The Mechatronic Systems Internet modeling method of transfer entropy.
Background technique
Process industry production system production equipment is various, and needs various auxiliary systems, between each structural unit constantly
The exchange of substance, information, energy is carried out, it is a distributed complex electromechanical systems that internal system conjunction coupling degree is high.It is multiple
Miscellaneous network is current research complication system structure, the most important theories of function and dynamic behavior.Network modelling is that complication system is built
The active direction that the important means and complex network area research of mould are earliest, achievement is most.In numerous network modellings
In method, the observation data of complication system is made full use of to obtain the information flow between different variables, building reflection complication system is dynamic
The complex network model of state evolved behavior is the topic of a common interest.The core of complication system information flow network model construction
The heart is accurately estimating to the information flow between variable, and more specifically, it includes two important indicators in direction and intensity.
Transfer entropy can be used for measuring oriented between two random processes as a kind of nonparametric statistical method for exempting from model
Amount of transmitted information is the important method that nonlinear system information flow is estimated.It is non-linear that Schreiber introduces transfer entropy measurement earliest
System information flows.Subsequent all kinds of technologies be used to estimate transfer entropy from system observation sequence.Symbolism is symbolic time series
The basis of analysis, it is related to converting original time series to series of discrete symbol.In many cases, discretization degree can
It can be quite serious.The global parameter based on global symbol extraction time sequence such as Wessel N., and pass through the relationship with parameter
To indicate each element.This global approach Shortcomings in terms of extracting partial detailed information and real-time performance.Staniek is answered
Original transfer entropy is improved with arrangement entropy symbolism method, symbol transfer entropy has been put forward for the first time, by ignoring details
Structure knot information is to reduce influence of the noise to observation sequence.On this basis, Papana etc. introduces partial symbols transfer entropy,
The orientation causality between each component of multi-variable system is analyzed, and proposes a kind of direct cause and effect of nonstationary time series
Framework of identification, but its still using arrangement entropy symbolism method.
The improvement done in these above-mentioned researchs to original transfer entropy has greatly pushed transfer entropy method real complicated
Application in system in Noise Data.However, original symbol transfer entropy is based on the symbolism principle for arranging entropy, only
It is put in order using vector element in time series phase space as symbolism, this symbolism principle is a kind of rough symbol
Change method may have lost the structural information of script time series, cause the information loss of original series, and then variation
Between interactive information accurately estimate.Therefore, how to ensure that the symbol sebolic addressing after symbolism expresses original series as far as possible
Structural information simultaneously improves the core content that its anti-noise ability is symbol transfer entropy and its Research of Improving Method.
Summary of the invention
The purpose of the present invention is to provide a kind of Mechatronic Systems Internet modeling side based on self-adaptive symbol transfer entropy
Method, with overcome the deficiencies in the prior art.
In order to achieve the above objectives, the present invention adopts the following technical scheme:
A kind of Mechatronic Systems Internet modeling method based on self-adaptive symbol transfer entropy, in multivariate space reconstruct
On the basis of obtain original time series symbolism common parameter, and using self-adaptive kernel density estimation method to original time sequence
The probability density and probability distribution of column are estimated, carry out equiprobability to original time series according to equiprobability division principle and draw
Point, on the basis of balanced symbol sebolic addressing is to the structural information loss of original time series and noise immunity, obtain optimal symbol
Number number and demarcation interval carry out the expression of coarse symbol to original time series, then to the symbol sequence of original time series
Column carry out transfer entropy analysis, and carry out the calculating of net amount of transmitted information, to obtain basic ginseng needed for system interaction network modelling
Number, to establish the network model of reflection real system bottom interaction mechanism.
Further, the variables set for needing the monitoring objective for the complex electromechanical systems analyzed is chosen, original time sequence is obtained
The common parameter of column symbolism, primordial time series data collection obtained are N number of monitored parameters i, pass through method of wavelet packet pair
Monitored parameters noise reduction obtains the time series after noise reduction, and calculates the Signal to Noise Ratio (SNR) of noise reduction presequencein；It is mutually empty by multivariable
Between reconstructing method calculate the Embedded dimensions m and delay time T of each pair of monitored parameters, as the public of each pair of monitored parameters symbolism
Parameter set (m, τ).
Further, variable monitors number after obtaining noise reduction using self-adaptive kernel density estimation method to each monitored parameters i
According to probability density function fi(x), according to probability density function fi(x) probability distribution F is obtainedi(x)。
Further, the probability distribution F that will be obtained using equiprobability division principlei(x) equiprobability division is carried out, and is combined
Obtained common parameter collection (m, τ) determines the symbolism parameter of each monitored parameters by optimization, obtains the symbol of time series
Change sequence；The symbolism sequence of each pair of monitored parameters carries out transfer entropy analysis, and the net information obtained between each pair of monitored parameters passes
The amount of passingUsing monitored parameters as node vi∈ V, the information transfering relation between monitored parameters are side ei∈ E, net information transmitting
AmountFor the weight w on sidei∈ W establishes the network model M of reflection complex electromechanical systems bottom interaction mechanismnet=(V, E,
W), to complete the modeling of the process industry complex electromechanical systems Internet.
Further, the symbol sebolic addressing obtained after self-adaptive symbolization conversion needs to carry out information biography to each pair of variable
Analysis is passed, and obtains the net amount of transmitted information between each pair of monitored parameters
The expression formula of transfer entropy is as shown in formula between monitored parameters；
In formula,For the information transfer entropy of Y to X,WithIt is i-th of value after sequence X and Y self-adaptive symbol, δ
It is the time delay between sequence X and Y.
Further, the information transfer entropy of X to Y
Net amount of transmitted informationSuch as following formula
Net amount of transmitted informationThe positive and negative direction as grid model directed edge of value, "+" indicate information transmitting
Direction is Y → X, and "-" indicates that information direction of transfer is X → Y,Weight w as directed edge in grid modeli。
Further, the determination of the characterization parameter of symbolism noiseproof feature: pass through noise coefficient NFCarry out quantitatively characterizing system
Noiseproof feature, expression formula are as follows:
Wherein SNRinFor input signal-to-noise ratio, SNRoutFor output signal-to-noise ratio；
The comentropy H (q) of the symbolism sequence formed after self-adaptive symbol meets H (q) > HL, HLFor under given information
Limit, using the noise minimum that semiosis introduces as optimization aim, i.e. the noise coefficient N of symbolism systemFMinimum optimization
Target obtains optimal glossary of symbols size qopt, the majorized function model of the process is as follows:
The size q of output symbol collection S after optimization process is exactly the optimal glossary of symbols S of semiosisoptSize
qopt, obtained glossary of symbols SoptIt can indicate are as follows:
Sopt=[0,1 ..., i ..., qopt-2,qopt-1]；
Monitoring time sequence samples are input to above-mentioned majorized function model, obtain optimal glossary of symbols SoptSize
qopt, and by the glossary of symbols S in the optimization processoptSize qoptIt is defeated that time series threshold space under corresponding divides point set P
Out, the threshold space optimal as time series divides point set Popt, optimal threshold space divides point set PoptExpression are as follows:
Optimal threshold space divides point set PoptAfterwards, space division is carried out to original time series, that is, be divided into
qoptA region, wherein division points PiTo Pi+1The probability for dividing region and the region for one is 1/qopt；Symbolism function table
It is as follows up to formula:
By the threshold function table in above formula, original time series can be converted to symbolism time series.
Compared with prior art, the invention has the following beneficial technical effects:
A kind of Mechatronic Systems Internet modeling method based on self-adaptive symbol transfer entropy of the present invention, in multivariate space
The common parameter of acquisition time sequence symbol on the basis of reconstruct, and using self-adaptive kernel density estimation method to original time
The probability density of sequence and distribution are estimated, and carry out equiprobability division to sequence according to equiprobability division principle, in equilibrium
On the basis of symbol sebolic addressing is to the structural information loss of original time series and noise immunity, chosen by constantly optimizing best
Symbol numbers and demarcation interval, the carry out coarse symbol expression of original series is realized, to improve between variable interaction
The accuracy of information measure carries out transfer entropy analysis to the symbol sebolic addressing of each pair of variable, and carry out net information biography on this basis
The calculating for the amount of passing with basic parameter needed for obtaining system interaction network modelling, and establishes reflection real system bottom interaction machine
The network model of system, the network model will be assessed for system mode, and fault propagation analyzes and diagnoses decision and provides foundation, to mention
The science of process industry complex electromechanical systems safe and reliable operation and intelligent decision making are horizontal under high complex working condition.
Further, time series guarantees maximum information stream between variable pair to using smallest embedding dimension number m and delay, τ
Detection, the arbitrary carry system through being adapted with glossary of symbols size are encoded and are decoded through the decimal system, are enormously simplified in transfer entropy analysis
Probability calculation complexity, so that improving information between variable pair transmits the accuracy and efficiency estimated.
Further,
Detailed description of the invention
Fig. 1 is time series equiprobability symbol division principle figure；Fig. 1 (a) is original signal, and Fig. 1 (b) and 1 (c) is frequency
Histogram and probability density curve based on AKDE, Fig. 1 (d) are cumulative probability density profile.
Fig. 2 is the sample tendency chart of Lorenz system variable X and Y；
Fig. 3 is influence of the symbol quantity to sequence information entropy in semiosis；
Fig. 4 is NF under different signal-to-noise ratio with the situation of change of symbol numbers；
Fig. 5 is the comparison diagram that arrangement entropy symbolism and self-adaptive symbol is respectively adopted in variable X and Y；Fig. 5 (a) is monitoring
Variable x carries out coding and decoding figure using arrangement entropy symbolism method；Fig. 5 (b) is that monitored parameters x is encoded using self-adaptive symbol
With decodingization method figure, Fig. 5 (c) is that monitored parameters y uses arrangement entropy symbolism method to carry out coding and decoding figure, and Fig. 5 (d) is
Monitored parameters y uses self-adaptive symbol coding and decodingization method figure；
Fig. 6 is noise when being 20dB, and TE, STE and ASTE calculate information and transmit variation tendency pair under different sliding windows
Than figure；
Fig. 7 is that TE, STE and ASTE calculate net information transmitting with the trend chart of sequence length；
Fig. 8 is the comparison diagram before and after 11 wavelet de-noising of monitored parameters；Fig. 8 a is effect picture before monitored parameters noise reduction, and Fig. 8 b is
Effect picture after monitored parameters noise reduction；
Fig. 9 is signal-to-noise ratio comparison of each variable of compressor set after wavelet de-noising；
Figure 10 is TE, and the comparison of STE and ASTE information transfer entropy: Figure 10 (a) variable 11 is used as source node；Figure 10 (b) becomes
Amount 11 is used as destination node；
Figure 11 is the net information transfer entropy comparison diagram that tri- kinds of methods of TE, STE and ASTE obtain: 11 conduct of Figure 11 (a) variable
Source node；Figure 11 (b) variable 11 is used as destination node；
System interaction network model when Figure 12 is compressor set normal service.
Figure 13 is present system flow chart.
Specific embodiment
The invention will be described in further detail with reference to the accompanying drawing:
As shown in figure 13, a kind of Mechatronic Systems Internet modeling method based on self-adaptive symbol transfer entropy of the present invention,
The common parameter of original time series symbolism is obtained on the basis of multivariate space reconstruct, and is estimated using self-adaptive kernel density
Meter method estimates the probability density and probability distribution of original time series, and according to equiprobability division principle to it is original when
Between sequence carry out equiprobability division, in balanced symbol sebolic addressing to the basis of the loss of the structural informations of original series and noise immunity
On, optimal symbol numbers and demarcation interval are chosen by constantly optimizing, coarse symbol table is carried out to original time series
Show, to improve the accuracy that interactive information between variable is estimated, on this basis, to original time series (each pair of monitored parameters)
Symbol sebolic addressing carry out transfer entropy analysis, and the calculating of net amount of transmitted information is carried out, to obtain needed for system interaction network modelling
Basic parameter, thus establish reflection real system bottom interaction mechanism network model.
Complex electromechanical systems Internet modeling method based on self-adaptive symbol transfer entropy, specifically includes the following steps:
Step 1), monitoring data and its pretreatment.Choose the variable for needing the monitoring objective for the complex electromechanical systems analyzed
Collection obtains the common parameter of original time series symbolism, and primordial time series data collection obtained is N number of monitored parameters i,
The time series after noise reduction is obtained to monitored parameters noise reduction by method of wavelet packet, and calculates the signal-to-noise ratio of noise reduction presequence
SNRin。
Step 2) calculates common symbol parameter based on the monitored parameters of multivariate phase space reconstruction.Pass through multivariable
State Space Reconstruction calculates the Embedded dimensions m and delay time T of each pair of monitored parameters, as each pair of monitored parameters i symbolism
Common parameter collection (m, τ)；
Step 3), the self-adaptive kernel density estimation of monitoring data sample: self-adaptive kernel density is used to each monitored parameters i
Estimation method obtains the probability density function f of monitored parameters sample data after noise reductioni(x), according to probability density function fi(x) from
And obtain probability distribution Fi(x)；
The optimization of step 4), each monitored parameters symbolism parameter of time series centering determines: being divided using equiprobability former
Step 3) estimation is then obtained into probability distribution Fi(x) carry out equiprobability division, and obtain in conjunction with step 2 common parameter collection (m,
The symbolism parameter that each monitored parameters τ) are determined by optimization, obtains the symbolism sequence of time series；Determine each monitoring
Most crucial in the symbolism parametric procedure of variable is that the size of determining glossary of symbols S and the threshold space of sequence divide point set P, this
Invention optimization obtains optimal symbolism parameter, mainly includes that glossary of symbols S size q and threshold space divide point set P, so that the time
Information loss of the sequence after symbolism is minimum, and noiseproof feature is optimal.
Information between step 5), the symbolism sequence of each pair of monitored parameters transmits analysis.To each pair of monitored parameters sample
The symbolism sequence that data obtain after symbolism carries out transfer entropy analysis, obtains the net information transmitting between each pair of monitored parameters
AmountThe symbol sebolic addressing obtained after self-adaptive symbolization conversion needs to carry out each pair of monitored parameters information transmitting analysis,
The expression formula of its transfer entropy is as shown in formula；
In formula,For the information transfer entropy of Y to X,WithIt is i-th of value after sequence X and Y self-adaptive symbol, δ
It is the time delay between sequence X and Y.In the present invention, in order to obtain the detection of maximum information flow, we are by maximum delay
Time δ obtains maximum value δmax。
Similarly, the information transfer entropy of our available X to Y
In order to simplify the expression of subsequent network model, we calculate net amount of transmitted informationSuch as following formula
In addition, net amount of transmitted informationThe positive and negative direction as grid model directed edge of value, "+" indicate information
Direction of transfer is Y → X, and "-" indicates that information direction of transfer is X → Y,Weight as directed edge in grid model
wi
Symbol quantity and information loss after time series symbolism have been comprehensively considered due to self-adaptive symbol transfer entropy.When
Between detection of the sequence to maximum information stream between monitored parameters pair is guaranteed using smallest embedding dimension number m and delay, τ, warp and glossary of symbols
The adaptable arbitrary carry system of size is encoded and is decoded through the decimal system, and the probability calculation enormously simplified in transfer entropy analysis is complicated
Degree, so that improving information between monitored parameters pair transmits the accuracy and efficiency estimated.
The Internet modeling of step 6), complex electromechanical systems.Using a certain monitored parameters therein as node vi∈ V, often
It is side e to the information transfering relation between monitored parametersi∈ E, net amount of transmitted informationWeight w as sidei∈ W establishes anti-
Reflect the network model M of complex electromechanical systems bottom interaction mechanismnetIt may be expressed as:
Mnet=(V, E, W)
In formula, V is the set of all nodes in network, and E is the set on all sides in network, and W is the weight on side in network
Set, to complete the modeling of the process industry complex electromechanical systems Internet.
Most important step is to carry out the expression of coarse symbol to original time series in the analysis of symbol transfer entropy, and herein
On the basis of carry out transfer entropy analysis.Assemble of symbol size is mainly determined in time series symbolism and in the reasonable of monitored parameters
Optimal Subspace partition point set is determined in value range, and demarcation interval can be determined by cut-point.Semiosis is used
Monitored parameters valued space division methods will affect subsequent symbolic series analysis, so the semiosis of monitored parameters must
The distribution characteristics that its sample must tightly be relied on adaptively is adjusted.
1) symbolism equiprobability division principle describes
In order to facilitate the description of method, herein using the example of actual compression unit vibration signal progress probability density division
It introduces, process is as shown in Figure 3.Wherein Fig. 1 (a) is original signal, and Fig. 1 (b) and 1 (c) is frequency histogram and is based on AKDE
Probability density curve, Fig. 1 (d) be cumulative probability density profile.When glossary of symbols is 4, according to equiprobability division principle,
Fig. 1 (d) is that mark cut-point be P1, P2, P3, P4 to cumulative probability density profile, therefore the threshold value of signal is just divided into 4
(q=4) a section, each section are expressed as symbol " 0 ", " 1 ", " 2 ", " 3 ".
The each monitored parameters symbolism parameter of time series centering takes optimization to determine, specifically includes the following steps:
(1) determination of the characterization parameter of symbolism noiseproof feature.By the noise coefficient NF (noise for introducing person in electronics
Coefficient: Noise Factor) carry out the noiseproof feature of quantitatively characterizing system.Its expression formula is
Wherein SNRinFor input signal-to-noise ratio, SNRoutFor output signal-to-noise ratio.The coefficient is also the noise-induced of characterization system simultaneously
One parameter of energy deterioration degree.It can be seen that the value is not to be the bigger the better, its value is bigger, illustrates to mix in transmission process
The noise entered is also bigger, reflects the undesirable of device or the characteristic of channel.
(2) foundation of symbolism optimization model.
The comentropy H (q) for the symbol sebolic addressing that the present invention is formed after guaranteeing self-adaptive symbol meets H (q) > HL(HLFor to
Determine information lower limit) under the premise of, using the noise minimum that semiosis introduces as optimization aim, the i.e. noise of symbolism system
Coefficient NFMinimum optimization aim obtains optimal glossary of symbols size qopt, the majorized function model of the process is as follows
The size q of output symbol collection S after optimization process, the value are exactly the optimal glossary of symbols S of semiosisopt's
Size qopt, obtained glossary of symbols SoptIt can indicate are as follows:
Sopt=[0,1 ..., i ..., qopt-2,qopt-1]
(3) the optimal symbolism conversion of monitoring time sequence.
Monitoring time sequence samples are input to above-mentioned majorized function model, obtain optimal glossary of symbols SoptSize
qopt, and by the glossary of symbols S in the optimization processoptSize qoptIt is defeated that time series threshold space under corresponding divides point set P
Out, the threshold space optimal as time series divides point set Popt, optimal threshold space divides point set PoptCan be with table
It is shown as
Optimal threshold space divides point set PoptLater, it next needs to carry out space division to original time series, i.e.,
It is divided into qoptA region.Since each region is continuously, so it can be determined with the section between division points.
Wherein division points PiTo Pi+1The probability for dividing region and the region for one is 1/qopt。
Symbolism function expression is as follows
By the threshold function table in above formula, original time series can be converted to symbolism time series, to be the time
Accurate, the quick calculating of transfer entropy lays the foundation between sequence.
The simulation sequence of Lorenz chaos system is analyzed
Illustrate the complete in complication system dynamic interaction network modelling of algorithm using typical non-linear chaos Lorenz system
Process application.Analogue system Lorenz system return, parameter and test sample data are illustrated first；Secondly, passing through
Add experiment of making an uproar, the ASTE method proposed be compared with existing TE, STE method, with illustrate proposed method
Applicability and advantage under noise circumstance.Finally, choose different initial conditions in the case where determining system parameter and generate simulation sequence,
Lorenz system dynamic interaction network model is constructed using ASTE method, this method is verified to being by the otherness of network structure
The characterization ability for initial value sensitivity feature of uniting.
(1) Lorenz system and its parameter declaration
Lorenz equation is in 1963 by the meteorologist Lorenz of famous American to study climate change, by right
Flow the research of experiment, three certainty First-Order Nonlinear Differential Equations of foundation.These three equations are the classics sides in chaos field
Journey, Lorenz system be also first performance strange attractor continuous dynamical system, due to its monitored parameters meaning it is bright
It is true and equation simple, it is had a decisive role in complication system simulation analysis.
The expression formula of Lorenz equation is as follows:
Wherein, selection σ=- 10, r=28, b=8/3 of parameter are positive real constant, and system is in chaos state at this time, determine
The chaos evolution process and characteristic of system.One group of initial value of given monitored parameters [X, Y, Z] is X=-1, Y=0, Z=1.So
Quadravalence Runge Kutla method is used afterwards, and time step is taken as 0.0l and is integrated, and obtains the time series of 3 monitored parameters
The simulation sequence that length is 35000.
(2) test sample data select
By choosing sample of preceding 2000 sequences of Lorenz system monitoring variable X and Y as analysis, for algorithm
Noiseproof feature analysis.Its Sequence Trend figure such as Fig. 2 is shown in it.
(3) the self-adaptive symbol process of time series pair
Feature is modeled according to grid, needs to analyze the interaction between each pair of monitored parameters.Especially to each
The phase space reconfiguration of variable, determine each monitored parameters sample sequence symbolism common parameter, it is close to be then based on self-adaptive kernel
Degree improved method obtains the optimal glossary of symbols size and its threshold space cut-point of each pair of monitored parameters, divides to its threshold space
And carry out Symbolic Representation.
(a) comentropy of symbol sebolic addressing
In order to inquire into influence of the symbolic number to symbolism, the comentropy of three classes sequence: original time series, symbol is compared
Sequence and coding and decoding sequence.Horig, HsymAnd HEDIt is their corresponding comentropies respectively.X semiosis shown in fig. 6
Comentropy curve has different symbolic numbers.
From the point of view of the comentropy trend in Fig. 6, with the increase of symbolism number, the comentropy of symbol sebolic addressing, which is presented, to be increased
Big trend.It therefore, cannot in other words cannot be simple according to comentropy in order to realize the optimum segmentation of monitored parameters threshold space
Size determine glossary of symbols S size q, need to determine in conjunction with other constraint conditions.
(b) noise measurement of sign process
The structure that may cause sequence in the semiosis of time series changes, this, which is equivalent to, introduces new noise.For
Noise may be introduced in measurement semiosis, carrys out the anti-noise of descriptor process using noise coefficient incorporated in the present invention
Ability.
Can be seen that from the variation tendency of noise coefficient shown in Fig. 4, it can be seen that signal-to-noise ratio be 10dB, 20dB,
When 30dB, when glossary of symbols S size q is between 2-21, tub curve is presented in noise coefficient, with the increase of noise intensity, noise
The reduction of coefficient, curve " basin bottom " tend to be flat；When symbol numbers are 10-12, noise coefficient obtains most each noise coefficient
Small value illustrates that influence of the noise intensity to the classifying rationally of monitored parameters threshold space is little, this also indicates that semiosis has
There is stronger consistency anti-noise ability.
The self-adaptive symbolization for can be changed X and Y and the comparison of arrangement entropy symbolism is shown in FIG. 5.Fig. 5 ratio is less
With the coding and decoding effect for the symbol sebolic addressing that time sequence symbol method generates: (c) being respectively monitored parameters x and y (a)
It is coded and decoded using arrangement entropy symbolism method；(b), it is respectively (d) monitored parameters x and y to be compiled with adopting self-adaptive symbol
Code and decodingization method.
As shown in figure 5, we can clearly have found, use self-adaptive symbol compared with arranging entropy symbolism method
The sequence that method obtains more accurately expresses the basic structural feature of original time series.
(4) the noiseproof feature analysis of algorithm
(a) impact analysis of the specific noise to distinct symbols transfer entropy method
Time series forms symbol sebolic addressing after self-adaptive symbol, and the transfer entropy calculating of symbol sebolic addressing is system interaction net
The basic work of network modeling.In order to verify the superiority of method proposed by the invention, ensuring length of time series holding one
In the case where cause, Lorenz variable is analyzed using traditional transfer entropy, symbol transfer entropy and ASTE method of the present invention
X, the interaction between Y and Z sequentially adds the Gauss white noise of 10dB, 20dB and 30dB in X the and Y sample sequence of selection
Noiseproof feature of the sound for algorithm is analyzed.
As shown in fig. 6, by comparative analysis have that transfer entropy method and symbol transfer entropy method calculate as a result, we are not difficult to send out
Now every kind of method can detect the interaction between Lorenz internal system monitored parameters.But come from the information content of transmitting
It says, the testing result that ASTE method obtains is apparently higher than STE and TE, this shows that ASTE method significantly improves the transmitting of information
Amount；From the point of view of the variation tendency of curve, the curvilinear trend that ASTE and STE method obtains is almost the same, this shows ASTE and tradition
STE algorithm performance be slightly better than TE, this mainly has benefited from the filtering of first two method symbolizationization, hence it is evident that improves the anti-of algorithm
Noise-induced and stability.So ASTE method be better than in terms of detection information amount, noise immunity and stability existing TE and
STE algorithm shows the symbolism optimization algorithm based on self-adaptive kernel density estimation, improves noiseproof feature, so that symbolism
The anti-acoustic capability of journey reaches optimal effect.
(b) impact analysis of the sequence length to self-adaptive symbol transfer entropy method
In order to further explore influence of the length of time series to the algorithm proposed, by using different length when
Between sequence data carry out when test.Fig. 7 is the comparison of length of time series symbol transfer entropy under particular noise condition
From Fig. 7's, it is apparent that monitored parameters sample is longer bigger for symbol transfer entropy calculated value.So being
Guarantee the balance between multivariable, it is necessary to rationally determine the sample length for participating in calculating every time, the i.e. window width of sliding window,
Here we analyze the sliding window length of X and Y for ASTE using 2500 length as monitored parameters.
The Internet modeling and analysis of actual compression unit
Using the monitoring data of certain coal chemical industry enterprises compressor set generated during normal service to involved by the present invention
And modeling method be described in detail.
The compressor set monitored parameters used in present example verifying are as shown in table 1:
The monitored parameters table of 1 compressor set of table
It is influenced to eliminate magnitude differences, noise on analysis system mode bring in DCS system acquisition data, to original
The process of data preprocessing with noise reduction process is normalized in beginning data.
The method of network modelling proposed according to the present invention needs to analyze the interaction between each pair of variable.System
System Internet modeling work mainly has, first the phase space reconfiguration to each monitored parameters, determines the public number of each symbolism
And independent parameter, it realizes the symbolism of time series, the transfer entropy of each pair of monitored parameters is analyzed on this basis.
Specifically mainly comprise the steps of:
(1) the self-adaptive symbol common parameter of status monitoring sequence solves
Using mutual information method and method, it is determined that the parameter of each monitored parameters phase space reconfiguration.In order to which variable centering is each
Monitored parameters are embedded into the phase space reconstruction with same dimension, guarantee that each monitored parameters are unfolded without distortion, according to public
Wherein m and τ is respectively public Embedded dimensions and time delay to reconstruction parameter altogether.Table 2 lists monitored parameters 11 and other monitorings
Multivariable the reconstruction parameter m and τ for the variable clock synchronization that variable is formed:
2 monitored parameters 11 of table form the public reconstruction parameter of variable pair with other each monitored parameters
It can be seen that the reconstruction parameter in table 2 between each pair of monitored parameters is not quite similar, embodying multivariable in expression is
Multi-dimensional nature when system state can make up deficiency of the unitary variant when describing system mode.
(2) the noise estimation of monitoring time sequence
The noise for including in monitoring data sequent can not only reduce the quality of signal, but also drastically influence at various correlations
The validity of adjustment method.So noise estimation is extremely important for various types of signal processing.The monitoring data in actual system
Noise is inevitable, and equalization information loss and noise resisting ability are needed during time series self-adaptive symbolization.This is just
It is required that the noise in initial data must sufficiently be estimated before data application, thus be the symbolism parameter of monitoring data sequent
Optimization, which determines, provides foundation.
The method of wavelet-packet noise reduction is used herein.Noise reducing of data process is divided into two steps of decomposition and reconstruct: 1. to not
After taking suitable wavelet basis function and Decomposition order with variable, with fixed threshold method to each wavelet details coefficient after decomposition
Carry out soft-threshold processing；2. reconstructing the last layer approximation coefficient and all layers of detail coefficients, the variable timing after obtaining noise reduction
Figure, as shown in Fig. 8 a, Fig. 8 b.
As shown in Figure 8, after normalized Noise reducing of data, the general trend of signal does not change, and has filtered part
High-frequency noise.It can be seen that sequential structure is more clear after noise reduction, the signal-to-noise ratio after each variable noise reduction is as shown in Figure 9.
As can see from Figure 9 in actual monitoring sequence, the level of each variable institute Noise is different.Original series
Noise evaluation result will provide foundation for the symbolism of time series.This is mainly reflected in, and each variable monitoring data sequent passes through
Optimization, obtains optimal symbol number and the respective threshold section of semiosis, generates symbol sebolic addressing most according to the division result
It can reflect the structure of sequence after noise reduction.
(3) optimal glossary of symbols and variable threshold space divide
Using time series self-adaptive symbol method proposed by the invention, to 16 prisons involved in present example
The monitoring data sequent for surveying variable carries out symbolism, and the size of the glossary of symbols of each variable is as shown in table 3.
The self-adaptive symbol glossary of symbols size of each variable of table 3
| Variable number | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 |
| Symbol numbers | 60 | 61 | 48 | 7 | 16 | 126 | 160 | 91 | 200 | 200 | 121 | 36 | 39 | 32 | 31 | 2 |
From table 3 it is observed that symbol numbers reflect the structural complexity of time series to a certain extent.Time sequence
The structure of column more complexity is higher, and the symbol numbers needed are more, otherwise the structure of time series is simpler, the symbol needed
Number is fewer.Available corresponding variable partitions point set after optimal glossary of symbols is obtained, to carry out symbol to time series
Changing indicates.
(4) symbol transfer entropy calculates
In order to verify the superiority of method proposed by the invention, using traditional transfer entropy, symbol transfer entropy and this hair
It is bright based on the improved symbol transfer entropy method of self-adaptive kernel density estimation analyze the variable 11 being most closely related with the failure and
Interaction between its dependent variable applies tradition TE and STE that is, using node 11 as source node and destination node respectively
And ASTE method calculates information transfer entropy, as shown in Figure 10 (a) and 10 (b).
In order to intuitively embody the asymmetry of interactive relation between node, Section 2.2 of 8 calculate node 11 of formula is used here
Net amount of transmitted information TE when respectively as source node and destination node between nodenet, as shown in figure 11.
It is mutual between variable 11 and its dependent variable to can be found that every kind of method can detect from Figure 11 (a) and 11 (b)
Effect.By comparing traditional TE method, STE method and ASTE method it can be found that the performance of STE method and ASTE method is obvious
Greater than transfer entropy (TE), what this showed symbol transfer entropy method has certain noiseproof feature.It is calculated by ASTE method
Node 11 and other network nodes between information transfer entropy be all larger than traditional TE and STE's as a result, this shows that ASTE method mentions
High information transmits the validity estimated.
(5) building of complex electromechanical systems military service Internet model
The ASTE analysis between each pair of variable is calculated by the above process, so that it is determined that between network node and its node
Weight and direction, be used for the network model building of system, constructed network model is as shown in figure 12.
Can intuitively it find out from the network model in Figure 12, the phase interaction in the network model established between each node
With a strong continune network is similar to, this shows in the real system course of work, system tight association, co-ordination, work
It is complex to make mechanism.In all nodes, have between the equal nodes of node 1,2,3,12,13,14,15 and other nodes relatively strong
Interaction, and other nodes is then relatively small, illustrates that these variables have in the failure of characterization system with the failure
It is representative.
By compared with the physical structure of each variable and meaning, it was demonstrated that the validity of information model.Based on to each change
The description of amount, variable 1,2 and 3 can reflect steam turbine condenser heat exchange property, and variable 12,13,14 and 15 is steam turbine bearing
The main monitoring of vibration, this variable parameter are the important evidences of feedback regulation and control during steam turbine operates normally.Therefore, the party
The information model that method is established meets known system operation mechanism, the reality for reflecting and being reconstructed between system components
Relationship.
Claims (7)
1. a kind of Mechatronic Systems Internet modeling method based on self-adaptive symbol transfer entropy, which is characterized in that in multivariable
The common parameter of original time series symbolism is obtained on the basis of Space Reconstruction, and utilizes self-adaptive kernel density estimation method pair
The probability density and probability distribution of original time series are estimated, carry out according to equiprobability division principle to original time series
Equiprobability divides, and on the basis of balanced symbol sebolic addressing is to the structural information loss of original time series and noise immunity, obtains
Optimal symbol numbers and demarcation interval carry out the expression of coarse symbol to original time series, then to original time series
Symbol sebolic addressing carry out transfer entropy analysis, and the calculating of net amount of transmitted information is carried out, to obtain needed for system interaction network modelling
Basic parameter, thus establish reflection real system bottom interaction mechanism network model.
2. a kind of Mechatronic Systems Internet modeling method based on self-adaptive symbol transfer entropy according to claim 1,
It is characterized in that, choosing the variables set for needing the monitoring objective for the complex electromechanical systems analyzed, original time series symbol is obtained
The common parameter of change, primordial time series data collection obtained are N number of monitored parameters i, are become by method of wavelet packet to monitoring
Amount noise reduction obtains the time series after noise reduction, and calculates the Signal to Noise Ratio (SNR) of noise reduction presequencein；Pass through multivariate phase space reconstruction
Method calculates the Embedded dimensions m and delay time T of each pair of monitored parameters, the common parameter collection as each pair of monitored parameters symbolism
(m,τ)。
3. a kind of Mechatronic Systems Internet modeling method based on self-adaptive symbol transfer entropy according to claim 2,
It is characterized in that, obtaining the general of variable monitoring data after noise reduction using self-adaptive kernel density estimation method to each monitored parameters i
Rate density function fi(x), according to probability density function fi(x) probability distribution F is obtainedi(x)。
4. a kind of Mechatronic Systems Internet modeling method based on self-adaptive symbol transfer entropy according to claim 3,
It is characterized in that, the probability distribution F that will be obtained using equiprobability division principlei(x) equiprobability division is carried out, and combines and obtains
Common parameter collection (m, τ) determines the symbolism parameter of each monitored parameters by optimization, obtains the symbolism sequence of time series；
The symbolism sequence of each pair of monitored parameters carries out transfer entropy analysis, obtains the net amount of transmitted information between each pair of monitored parametersUsing monitored parameters as node vi∈ V, the information transfering relation between monitored parameters are side ei∈ E, net amount of transmitted informationFor the weight w on sidei∈ W establishes the network model M of reflection complex electromechanical systems bottom interaction mechanismnet=(V, E,
W), to complete the modeling of the process industry complex electromechanical systems Internet.
5. a kind of Mechatronic Systems Internet modeling method based on self-adaptive symbol transfer entropy according to claim 4,
It is characterized in that, the symbol sebolic addressing obtained after self-adaptive symbolization conversion, needs to carry out each pair of variable information transmitting analysis,
And obtain the net amount of transmitted information between each pair of monitored parameters
The expression formula of transfer entropy is as shown in formula between monitored parameters；
In formula,For the information transfer entropy of Y to X,WithIt is i-th of value after sequence X and Y self-adaptive symbol, δ is sequence
Arrange the time delay between X and Y.
6. a kind of Mechatronic Systems Internet modeling method based on self-adaptive symbol transfer entropy according to claim 5,
It is characterized in that, the information transfer entropy of X to Y
Net amount of transmitted informationSuch as following formula
Net amount of transmitted informationThe positive and negative direction as grid model directed edge of value, "+" indicate information direction of transfer
For Y → X, "-" indicates that information direction of transfer is X → Y,Weight w as directed edge in grid modeli。
7. a kind of Mechatronic Systems Internet modeling method based on self-adaptive symbol transfer entropy according to claim 2,
It is characterized in that, the determination of the characterization parameter of symbolism noiseproof feature: passing through noise coefficient NFCarry out the noise of quantitatively characterizing system
Performance, expression formula are as follows:
Wherein SNRinFor input signal-to-noise ratio, SNRoutFor output signal-to-noise ratio；
The comentropy H (q) of the symbolism sequence formed after self-adaptive symbol meets H (q) > HL, HLFor given information lower limit, with
The noise minimum that semiosis introduces is as optimization aim, i.e. the noise coefficient N of symbolism systemFMinimum optimization aim,
Obtain optimal glossary of symbols size qopt, the majorized function model of the process is as follows:
The size q of output symbol collection S after optimization process is exactly the optimal glossary of symbols S of semiosisoptSize qopt,
Obtained glossary of symbols SoptIt can indicate are as follows:
Sopt=[0,1 ..., i ..., qopt-2,qopt-1]；
Monitoring time sequence samples are input to above-mentioned majorized function model, obtain optimal glossary of symbols SoptSize qopt, and
By the glossary of symbols S in the optimization processoptSize qoptTime series threshold space under corresponding divides point set P output, as
The optimal threshold space of time series divides point set Popt, optimal threshold space divides point set PoptExpression are as follows:
Optimal threshold space divides point set PoptAfterwards, space division is carried out to original time series, that is, is divided into qoptIt is a
Region, wherein division points PiTo Pi+1The probability for dividing region and the region for one is 1/qopt；Symbolism function expression
It is as follows:
By the threshold function table in above formula, original time series can be converted to symbolism time series.
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